How did an English person get entry to East Germany during the Cold War?

Here is some anecdotal evidence. A friend of mine travelled to East-Berlin during the late part of the cold war. He's a Swedish citizen and he travelled using a tourist visa. Don't know how hard it was to get, but I think they wanted tourists for currency and propaganda.

He went by train and said that when the train stopped in West-Berlin all the tourists got off and it was just him and a few businessmen on the train. Then a grumpy border guard entered and demanded "Papire, bitte!" and when he saw that he travelled on a tourist visa he suddenly became very happy. "Ah, jungen touriste!".

He also claimed he was the only one to write graffiti on the eastern side of the Berlin wall so he may not have been entirely reliable.

For any visit for staying overnight, a form of package tour had to be organized by the Reisebüro der DDR

• unless you were invited by relatives of on business

A visa would then be issued at the border, based on the papers issued by the Travel Agent (on behalf of the Reisebüro der DDR) or by the Volkspolizei for private visits.

Exception: day visits to East-Berlin or a Tourist bus tour to Potsdam, where a permit (1977 Visa with a DM 5 fee) would be issued at the border.

Day visits outside of East-Berlin were only possible for residents of West-Berlin, when they were applied for beforehand.

For all day visits, the same crosspoint you used to enter had to be used for exit.

Order from 22 December 1976, Ministry of State Security (Stasi)
Introduction of Visa requirements for non Socialist citizens ...
...

• die Ausreise hat bis 24.00 Uhr des Ausstellungstages des Visums über die Grenzübergangsstelle zu erfolgen, über die die Einreise erfolgte ;

• the departure must be made by 24.00 on the day of issue of the visa through the border crossing point through which the entry was made; ...

• Order contains all other regulations, referencing those that have not changed

Although there were some extra regulations for German citizens, these rules otherwise applied for all westerners.

Q: How did an English person get entry to East Germany during the Cold War?

Just crossing the border, ignoring all East-German border guards!

That may have been as simple that. Really.

Angering all of those East-Germans, to be sure. In Berlin, at crossing Friedrichstraße, Checkpoint Charlie.

On August 2, 1989, the "Berliner Zeitung" newspaper, which appeared in the eastern part of the city, reported that the East Berliners would be annoyed by the visits of Allied soldiers from the West, using a report from the German Press Agency (dpa): "Anyone who explores the surroundings of the 'Centrum' department store at the main railway station on Saturdays, for example, will easily find several British private cars and British military buses. In front of the 'Centrum' department store at Alexanderplatz there are two French military buses and three American ones. And then, with their tartan skirts and tight calves, a few 'Highlanders' march through the socialist consumer paradise.

That's because in Berlin the Western allies insisted that they were always allowed to 'inspect' the Eastern half of the city. Without any interference of not sovereign lackeys of the Soviets: meaning an East-German border guard could tell them squat. If the GDR-guards would try something funny, they were usually ignored, Westerner insisting to speak only to their masters.

Well, once they did try something funny. The result was: (src)

This image from October 1961 is always used in documentaries to illustrate American defiance after the wall was being build. But it was nothing like that. The tank stand-off came after E Allan Lightner wanted to return unhindered - as usual – from a night at the opera in East Berlin. After being asked for papers the result was the above; and shortly later the Soviet admission of guilt, Lightner's return and continued business as before:

If in uniform, any English could go to Checkpoint Charlie and visit the East. Some formalities with his regiment beforehand to know his whereabouts and presumably prevent defection. But the uniform was really optional. No uniform meant just to show a waver card and otherwise do the same.

From there it gets funny. Travel recommendations for soldiers said to "prefer U-Bahn but don't take any S-Bahn". Why? Because the S-Bahn would take drunken strangers out of Berlin, a thing not covered by 4-powers Berlin-status. But the point is that that could happen easily.

The starting quote illustrates that this option was used extensively during the 80s, especially by US troops. Since after Nixon cancelled Bretton-Woods the Dollar got so weak that they would prefer shopping and partying in the East.

–– Berlin crisis: the standoff at Checkpoint Charlie
–– Stefanie Eisenhuth: "Freizeit Beim Feind. US-amerikanische Soldaten in Ost-Berlin", Zeithistorische Forschungen/Studies In Contemporary History, Vol 15, 2018, (p11–39).

This is of course not the typical case for non-soldiers. But there are mainly three very different scenarios to observe: allied soldiers in Berlin or on their way to Berlin, diplomats or 'diplomats' (the latter being 'peace scouts' eg ordinary spies) and non-military private citizens. For the last scenario I refer to other answers here.